Numerical Optimization Technique of Multilayer SERS Substrates

Round 1

Reviewer 1 Report

The manuscript presents a novel approach to characterize the efficiency of SERS substrates. The authors suggest using the Purcell factor and discuss the reasoning behind their suggestion. A numerical optimization technique of a three-dimensional (3D) SERS substrate with the finite element analysis is proposed. It is also shown the advantages of using 3D structure of carbon nanotubes (CNT) as a tree for nanoparticles strongly improves the SERS signal.

The authors may want to explain their suggestion better. Purcell factor is the ratio between the radiative decay rate near a cavity and radiative decay rate in the free space. The emission enhancement for emitters near metal particles has very different distance dependence relative to SERS due to the quenching mechanism. Also, the referred paper [28] uses local fields approach to calculate enhancement factor.

The following statement presents literature approach in a simplified way:  “Searching for “hot spots” and assessing the local fields at these points can provide relevant information about the SERS signal only in simple cases when all emitters are under the same conditions and therefore the field intensity at the different “hot spots” is the same. This is the case only for two-dimensional SERS substrates [13].”

It is too simplified, indeed. Typically, people imply inhomogeneous distribution of the local field and then numerically average the local field enhancement factor.

Technical issues:

-Something is missed here: “Due to the extremely high practical significance of the effect fundamental SERS theory is behind in development in compare with applied studies [18–20].”

-Equation 2 should be corrected: there is no incident field at scattered frequency in the denominator.

-Fig.1 caption does not describe the a) and b) pannels.

Quality of English is Ok.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The paper “Numerical optimization technique of multilayer SERS substrates” by A. Kadochkin et al. is devoted to the development of 3D structures with enhanced SERS activity. Both numerical and experimental results are provided. The authors found that the use of the third spatial dimension does not lead to saturation but to a proportional increase of the SERS signal. The authors found that the Purcell factor is a suitable function that determines the quality of the SERS substrate. The results of the paper are interesting and worth publishing.

There are some unclear places in the text:

11)      How photographs in Figure 5 are obtained? It is not explained in the text.

22)      What is the ‘lattice constant’ indicated in Figure 3? The main text of the paper does not mention any lattice constants.

Some other minor remarks:

1) I believe that all abbreviations in the text should be spelled out. That includes such acronyms as SERS.

2) The text of the manuscript contains several unclear sentences and phrases that should be rewritten, and English should be improved. Some of the unclear places are at the lines 24-25, 29-30, 39-40, 152-153.

These issues have been corrected, the paper can be published in the Photonics journal.

The English should be improved. See my above comments. The authors should carefully read their manuscript.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

In this article, the authors propose a three-dimensional SERS substrate numerical optimization technique based on finite element analysis. Using the optical reciprocity theorem, it is shown that instead of the well-known local field enhancement criterion it is more correct to use the Purcell factor as an objective function that determines the quality of the SERS substrate. It has been shown both theoretically and experimentally that shift from a planar substrate with a monolayer of nanoparticles to a 3D CNT structure acting as a substrate for nanoparticles makes it possible to increase the SERS signal. I believe that publication of the manuscript may be considered only after the following issues have been resolved.

1.    In order to highlight the advantages of this work, it is recommended that the author supplement a comparative table of related work.

2.    In the introduction section, it is recommended that the author delete the relevant formulas and add them to the appropriate section of the main text.

3.    In the simulation section of the article, the author needs to provide more detailed details, such as boundary conditions, mesh generation, structural parameters, etc.

4.    What is the Raman enhancement factor of this SERS device? Suggest the author to provide.

5.    Regarding the electric field enhancement devices, some of the latest relevant literature authors need to mention, such as Diamond & Related Materials 140 (2023) 110481; Opto-Electron Adv 4, 210048 (2021); Micromachines 2023, 14(9), 1802; Opto-Electron Adv 6, 230007 (2023).

6.    The English expression of the whole article needs to be further improved.

Minor editing of English language required

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

For this reviewer, it is interesting to consider the Purcell factor for the numerical study of SERS EF in this work. There needs to be uniformity and description in the terminology and graph format, making key points difficult to follow. However, this manuscript would be appropriate for the publication after the major revision, including the following:

1. The author should increase the size of the texts in Figure 2a 2. The author should use the same terms instead of using different terms (lattice constant, period, and gap).

3. The author should show which markers belong to which gaps in the legend box in Figure 4a.

4. The author needs to explain why they checked different set of gaps between particles in Figure 4a. For comparison, why didn’t the author simulate the same set of gaps? The number of layers, considered in Figure 4a without a clear definition of the term, are only up to 12 layers, but the author considered up to 20 layers in Figure 4b and c. They should show the same number of layers for better comparison.

5. The scale in the radiated power axis is different in all figures 4a, b, and c. The author should use the same scale.

6. Why are there only fitting lines and no markers in Figure 4b?

7. This reviewer thinks the experimental data do not clearly support the numerical simulation and strongly recommends that the author excludes all the experimental data in this manuscript. Correction of the number density, size, interparticle gap, and substrate effect of two systems is challenging and is beyond the scope of this research.

Fine

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Accept.

Author Response

We thank the Reviewer

Reviewer 4 Report

The current experimental data does not support the numerical simulation. The author must exclude all the discussion on experimental SERS study (on Si and CNT) or the author must show all the TEM based studies, including the number density,  size, and interparticle gap of NPs and the substrate effect (conductance....).

Author Response

We thank the Reviewer for his work. We have significantly revised the manuscript, the section regarding experiment has been removed, the detailed comparison of numerical calculations with experimental data will be published in future works. All the sections mentioned by the reviewer have been rewritten. We have also reconsidered the structure of the manuscript and have also rewritten the section “Discussion.”

Round 3

Reviewer 4 Report

This revised manuscript can be published in Photonics as it is.